You should get an email from MS (assuming you have a current Live account) that tells you that Live Messenger is no longer supported and that you need to switch to Skype. The email will give you a link to download the current version of Skype.

When you do this and install it the installer says it will move all your Messenger contacts to Skype and delete Messenger. This is exactly what happens. When you open Skype all your Messenger contacts will be there and everything will work OK - just the interface is different.

When I did the Skype install there was no shortcut installed so I just chenged my Messenger shortcut to point to Skype.